Find the domain of the function $z(x) = \sqrt[3]{x - 1} + \sqrt[3]{8 - x}.$
Explanation: Since we can take the cube root of any real number (positive or negative), $z(x) = \sqrt[3]{x - 1} + \sqrt[3]{8 - x}$ is defined for all real numbers $x.$  Thus, the domain of $z(x)$ is $\boxed{(-\infty,\infty)}.$